In telecommunication systems, squaring circuits are useful in a variety of contexts. For example, since squaring a wave changes its frequency in a signal receiver, a squaring circuit is useful for shifting the frequency range ("band") of an incoming modulated carrier wave to a different frequency range. Such shifting is useful in many situations. In particular, it is useful in modems at a receiver where it is desired to process the information on a pulsed carrier wave emanating from a transmission channel in which the information is coded as symbols represented by means of phase modulation of the pulses on the carrier. That is, the carrier is modulated by the (typically non-rectangular) pulses, and these pulses are periodic except for a separate phase shift that is imposed upon each pulse in accordance with the symbol corresponding to that pulse, whereby the pulse contains information. In such cases, among other things, it is desired at the receiver to determine the symbol rate--i.e., to achieve "timing recovery"--by first squaring the incoming modulated carrier wave by means of a squaring circuit in order to produce or enhance the energy component at the symbol rate prior to further signal processing, the phase modulated pulsed carrier itself as it emanates from the channel containing little or no energy at the symbol rate. As is known in the art, it is important in these cases that the output of the squaring circuit be pure. That is, it is important that the output produced by the squaring circuit be free of all odd-power terms, i.e., be free of all frequency components that have frequencies equal to odd-integer multiples of the input frequency, as well as be free of all even-power terms of higher order than the second. Otherwise, confusion would be introduced by the squaring circuit into the determination ("recovery") of the symbol rate.
In U.S. Pat. No. 4,585,961, issued on Apr. 29, 1986, to S. J. Daubert entitled "Semiconductor Integrated Circuits for Squaring a Signal with Suppression of the Linear Component," a squaring circuit having a pure output is disclosed. The circuit contains a pair of matched substantially identical paths to which an input voltage is applied. Each of the paths consists of a double-ended difference amplifier, which receives the input voltage and a dual-to-single-ended converter, which receives the output of the difference amplifier and delivers its own single-ended output to a nonlinear/summing device--such as a squarer/summer network--for nonlinearly transforming and summing the single-ended outputs of the converters in the two paths. Although the Daubert squaring circuit is useful for many purposes, nevertheless, because its MOS transistors operate in saturation and hence its output contains a relatively large d.c. offset (a relatively large term of zero order), an added voltage level shifter is needed in those cases where the output of the squaring circuit is used to drive another circuit in which this offset is undesirable, for example, another circuit in which all signals are referenced to ground, as in switched-capacitor filters and continuous-time filters. It would be desirable to have a squaring circuit without a dc offset and hence without the need for the added level shifts, because it consumes an undesirable amount of semiconductor chip area.